Consider a disk at center at $(0,0)$ of radius, $r$ $B_r(0)$ in the complex plane. Let $w_1$ and $w_2$ be two complex numbers belong to the disk $B_r(0)$. Consider a scheme,
$$w_k=\frac{a}{w_{k-1}}+\frac{b}{w_{k-2}}$$ $k=1,2,3,\dots,$
How can we determine the radius $R$ of the disk $B_R(0)$ such that $w_k \in B_R(0)$ for all k?